class Solution {
public:
    int minFallingPathSum(vector<vector<int>>& matrix)
    {
        int m = matrix.size(), n = matrix[0].size();
        vector<vector<int>> dp(m + 1, vector<int>(n + 2, INT_MAX));
        for (int j = 0; j < n + 2; j++) dp[0][j] = 0;
        for (int i = 1; i <= m; i++)
        {
            for (int j = 1; j <= n; j++)
            {
                int tmp = min(dp[i - 1][j - 1], dp[i - 1][j]);
                dp[i][j] = min(tmp, dp[i - 1][j + 1]) + matrix[i - 1][j - 1];
            }
        }
        int dpmin = INT_MAX;
        for (int i = 1; i <= n; i++)
        {
            dpmin = min(dpmin, dp[n][i]);
        }
        return dpmin;
    }
};